RAC 'attachments'

From the RAC Tracer Cards you can see my Dad was 'attached', moved to other units. Would his badges have changed according to the unit? I have looked at badges for all the units mentioned - I only have the ERY and RAC badges - nothing for the 7 Hussars or 3/4 C of L.
I mentioned in an earlier post that I have a photograph somewhere with a collar badge that shows crossed lances, nothing like either the Hussars or 3/4 C of L.

If he was entitled to wear any off these badges, which should I obtain? particular confused over 3/4 City of London, some of them have either 3 with 'south africa' 1900-1902 on them, the other has 4 and 'sharpshooters'. I have not seen a 3/4 City of London badge.

6/3/46 37 ORs from East Riding Yeomanry posted to 3/4th CLY.

I have tried searching this site for both 7 Hussars and 3/4 City of London. I am told nothing found. Help.